Whisk together flour, cocoa powder, baking soda, and salt in a medium bowl; set aside. Melt coarsely chopped chocolate with the butter in a small heatproof bowl in a double-boiler or in the microwave, stirring frequently.
Once melted, transfer chocolate mixture to the bowl of an electric stand mixer fitted with the paddle attachment. Add sugar, eggs, and vanilla; mix on medium speed until combined. Reduce speed to low; gradually mix in flour mixture. Fold in chocolate chips.
Form batter into heaping tablespoon-fulls, then roll into balls. Roll each ball in the crumbled Oreos until covered, then place the dough balls 2 inches apart on parchment-lined baking sheets. Bake until cookies are flat and surfaces begin to crack, about 12-15 minutes. (*Do not overbake these, or they will totally dry out!*) Transfer on parchment to wire racks and let cool.
Serve immediately, or store in a sealed container for up to 3 weeks.